An explicit relativistic light-front quark model in which the momentum
-transfer-dependent form factors of weak hadronic currents for transit
ions between heavy pseudoscalar and vector mesons is calculated in the
entire accessible kinematical region 0 less than or equal to q(2) les
s than or equal to q(max)(2) is formulated. Equal-time wave functions
corresponding to the updated version of the Isgur-Scora-Grinstein-Wise
model are used in a numerical investigation of to the updated version
of the Isgur-Scora-Grinstein-Wise model are used in a numerical inves
tigation of the semileptonic decays B --> D(D)lv(l), B --> pi(rho)lv(
l), D --> K(K)lv(l), and D --> pi(rho)lv(l). From available experimen
tal information about the branching fi actions Br(B --> Dlv(l)) and B
r(B --> rho lv(l)), the Cabibbo-Kobayashi-Maskawa parameters V-cb and
V-ub are estimated to be \V-cb\ = 0.036+/-0.002 and \V-ub\ = 0.0033+/-
0.0004. The model is further tested by comparing its predictions with
experimental data, QCD sum rules, and lattice calculations.